2018 AMC 10B Problem 2

Question

Sam drove

96

miles in

90

minutes. His average speed during the first

30

minutes was

60

mph (miles per hour), and his average speed during the second

30

minutes was

65

mph. What was his average speed, in mph, during the last

30

minutes?

64

65

66

67

68

Distance = rate

\times

time, and each

30

-minute leg is half an hour

Subtract the distance covered in the first hour from

96

to get the last leg’s distance

Each leg is half an hour. In the first, Sam drove

60 \cdot \tfrac12 = 30

miles; in the second,

65 \cdot \tfrac12 = 32.5

miles. That’s

62.5

miles so far. That leaves

96 - 62.5 = 33.5

miles for the last half hour, which is a speed of

\frac{33.5}{\tfrac12} = 67

mph. Therefore, the answer is D.

Problem 2 in other years